[Math] For the differential equation does the existence/uniqueness theorem guarantee that there is a solution to this equation through the point

calculusordinary differential equationspartial derivative

For the differential equation $\frac{dy}{dx}=\sqrt{y^2-25}$ does the existence/uniqueness theorem guarantee that there is a solution to this equation through the point

  1. (-1,28)

  2. (0,5)

  3. (3,-5)

  4. (1,34)

given that $\frac{dy}{dx}=f(x,y)=\sqrt{y^2-25}$

$f'=\frac{2y}{\sqrt{y^2-25}}$

this means as existence and uniqueness theorem the interval containing 5 is not have solution i am right

Best Answer

On solving the differential equation, we get $$\ln|y+\sqrt{y^2-25}|=x+c$$ Now if you put the $4$ points here, do you get real finite values of $c$?

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